12 papers · 1 filter
p-adic elliptic polylogarithms and cubic Chabauty
Jennifer S. Balakrishnan, Francesca Bianchi, Netan Dogra
The Chabauty--Coleman--Kim method, under favourable circumstances, describes the set of integral points of a hyperelliptic curve inside the -adic zeroes of certain transcendenta…
Generalised height pairings and the Albanese kernel
Netan Dogra
The Chabauty--Coleman--Kim method in depth two describes the rational points on a curve in terms of a generalisation of Nekovář's -adic height pairing which replaces $\mathbb{G}…
-adic approaches to unlikely intersections
Netan Dogra
In this article we explain the Buium--Coleman approach to the Manin--Mumford conjecture, and outline its generalisations. As an illustration, we give a -adic proof of a theorem…
A Buium--Coleman bound for the Mordell--Lang conjecture
Netan Dogra, Sudip Pandit
For a hyperbolic curve of genus with good reduction at , we give an explicit bound on the Mordell--Lang locus , when …
2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves II
Netan Dogra
We give refined methods for proving finiteness of the Chabauty--Coleman--Kim set , when is a hyperelliptic curve with a rational Weierstrass point. The mai…
The Zilber--Pink conjecture for products of curves with highly degenerate reduction
Netan Dogra
We give a proof of the Zilber--Pink conjecture for -fold self-products of a curve inside the self-product of its Jacobian, when has appropriate bad reduction, its Jacobi…